Method of manufactured solutions code verification of elastostatic solid mechanics problems in a commercial finite element solver

•Examples of rigorous code verification for solid mechanics are rare in literature.•Verification evidence is especially lacking for nonlinear analyses and commercial codes.•We use the method of manufactured solutions (MMS) to verify a commercial code.•Common linear and nonlinear elastostaic problems...

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Bibliographic Details
Published in:Computers & structures Vol. 229; p. 106175
Main Authors: Aycock, Kenneth I., Rebelo, Nuno, Craven, Brent A.
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.03.2020
Elsevier BV
Subjects:
Code verification
Computer simulation
Constitutive models
Convergence
Deformation analysis
Elastostatics
Finite element analysis (FEA)
Finite element method
Grid refinement (mathematics)
Mathematical models
Mechanics
Method of manufactured solutions (MMS)
Nonlinear analysis
Solid mechanics
Source code
Verification
Verification and validation (V&V)
Method of manufactured solutions (MMS)
Verification and validation (V&V)
Finite element analysis (FEA)
Code verification
ISSN:0045-7949, 1879-2243
Online Access:Get full text
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Summary:•Examples of rigorous code verification for solid mechanics are rare in literature.•Verification evidence is especially lacking for nonlinear analyses and commercial codes.•We use the method of manufactured solutions (MMS) to verify a commercial code.•Common linear and nonlinear elastostaic problems are considered.•We observe second-order displacement and first-order stress and strain convergence.•Source code and simulation files are provided to facilitate future MMS studies. Much progress has been made in advancing and standardizing verification, validation, and uncertainty quantification practices for computational modeling in recent decades. However, examples of rigorous code verification for solid mechanics problems in literature remain scarce, particularly for commercial software and for the non-trivial large-deformation analyses and nonlinear materials typically needed to simulate medical devices. Here, we apply the method of manufactured solutions (MMS) to verify a commercial finite element code for elastostatic solid mechanics analyses using linear-elastic, hyperelastic (neo-Hookean), and quasi-hyperelastic (Hencky) constitutive models. Analytical source terms are generated using Python/SymPy and are implemented in ABAQUS/Standard without modification to solver source code. Source terms for the three constitutive models are found to vary nearly six orders of magnitude in the number of mathematical operations they contain. Refinement studies reveal second-order displacement and first-order (or higher) stress and strain convergence in response to mesh refinement for all constitutive models and first-order displacement convergence in response to pseudo-time increment refinement for the Hencky-elastic case. We also investigate the sensitivity of convergence order to quantitatively minor changes to the underlying mathematical model using an exploratory case. Code used to generate the MMS source terms and simulation input files are provided as Supplemental Material.
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2019.106175